Uncertain Fuzzy Reasoning: A Case Study in Modelling Expert Decision Making

Abstract

Abstract-This paper presents a case study in which the introduction of vagueness or uncertainty into the membership functions of a fuzzy system was investigated in order to model the variation exhibited by experts in a medical decision-making context. A conventional (type-1) fuzzy expert system had previously been developed to assess the health of infants immediately after birth by analysis of the biochemical status of blood taken from infants' umbilical cords. Variation in decision making was introduced into the fuzzy expert system by means of membership functions which altered in small, predetermined manners over time. Three types of variation in membership functions were investigated: i) variation in the centre points, ii) variation in the widths, and iii) the addition of "white noise." Different levels (amounts) of uniformly distributed random variation were investigated for each of these types. Monte Carlo simulations were carried out to propagate the variation through the inferencing process in order to determine distributions of the conclusions reached. Interval valued type-2 fuzzy systems were also implemented to investigate the boundaries of variability in decisions. The results obtained were compared to the experts' decisions in order to determine which type and size of membership function variability best matched the experts' variability. The novel reasoning technique introduced in this study is termed nonstationary fuzzy reasoning.Index Terms-Interval type-2 fuzzy expert systems, medical decision making, nonstationary fuzzy reasoning, nonstationary type-1 fuzzy expert systems, umbilical acid-base assessment.

Fuzzy Expert Systems (FES) for Medical Diagnosis

“…76 The other areas of applications of fuzzy logic are: prediction of aneurysm, fracture healing 77,78 and in nonstationary FES, intuitionistic fuzzy sets. 79,80 The Fuzzy Expert System has proved its usefulness significantly in the medical diagnosis for the quantitative analysis and qualitative evaluation of medical data, consequently achieving the correctness of results. The computer based diagnostic tools and knowledge base certainly helps for early diagnosis of diseases.…”

On Constructing Parsimonious Type-2 Fuzzy Logic Systems via Influential Rule Selection

“…In a type-2 fuzzy inference system (T2FIS), some fuzzy sets used in the antecedent and/or consequent parts and each rule inference output are type-2 fuzzy sets. T2FISs have been used in many successful applications in various areas where uncertainties occur, such as in decision making [6]- [8], diagnostic medicine [9], [10], signal processing [11], [12], traffic forecasting [13], mobile robot control [14], pattern recognition [15]- [17], intelligent control [18], [19], and ambient intelligent environments [20].…”

Type-1 OWA operator based non-stationary fuzzy decision support systems for breast cancer treatments

“…However, it has often been demonstrated, particularly in breast cancer decision making, that groups of experts exhibit both intra-expert variability and inter-expert variability [6], [7]. Intra-expert variability is exhibited when an individual expert's decisions, given the same problem (i.e.…”

“…Inter-expert variability is exhibited when a group or panel of experts differ in their decisions in a particular situation (when faced with the same data). Recently, non-stationary fuzzy sets have been proposed to model this sort of variation [7], in which variability is introduced into the membership functions of a fuzzy set through the use of random alterations to the parameters of generating function(s). In this way, the membership function of a non-stationary fuzzy set may alter over time.…”